Solve and graph the following absolute value inequalities.
(B) $\mid 6x-9\mid -7\le -7$

• A. $x=1.5$
• B. $x=-1.5$
• C. $[-1.5,1.5]$
• D. $(-1.5,1.5)$

Answer: (A)

Verified step by step guidance

1. Start with the given inequality: \(\left|6x - 9\right| - 7 \leq -7\).
2. Add 7 to both sides to isolate the absolute value expression: \(\left|6x - 9\right| \leq -7 + 7\).
3. Simplify the right side: \(\left|6x - 9\right| \leq 0\).
4. Recall that the absolute value of any expression is always greater than or equal to zero, so \(\left|6x - 9\right| \leq 0\) means \(\left|6x - 9\right| = 0\).
5. Set the expression inside the absolute value equal to zero and solve for \(x\): \$6x - 9 = 0$.